To determine the probability that Peter rolls an even number on a standard 6-sided dice, follow these steps:
1. Identify Total Outcomes:
- A standard 6-sided dice has faces marked 1, 2, 3, 4, 5, and 6. This means there are 6 possible outcomes in total.
2. Identify Favorable Outcomes:
- The even numbers on a 6-sided dice are 2, 4, and 6. Hence, there are 3 favorable outcomes.
3. Calculate the Probability:
- Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes:
[tex]\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\][/tex]
- Substituting the numbers into the formula:
[tex]\[
\text{Probability} = \frac{3}{6}
\][/tex]
4. Simplify the Fraction:
- Simplifying [tex]\(\frac{3}{6}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor (which is 3), we get:
[tex]\[
\frac{3 \div 3}{6 \div 3} = \frac{1}{2}
\][/tex]
5. Convert to Decimal:
- Convert the fraction [tex]\(\frac{1}{2}\)[/tex] to a decimal:
[tex]\[
\frac{1}{2} = 0.5
\][/tex]
Therefore, the probability that Peter rolls an even number on a 6-sided dice is [tex]\(0.5\)[/tex].
